The Time Complexity of Constraint Satisfaction
- 6 May 2008
- book chapter
- conference paper
- Published by Springer Science and Business Media LLC
Abstract
We study the time complexity of (d,k)-CSP, the problem of deciding satisfiability of a constraint system Open image in new window with n variables, domain size d, and at most k variables per constraint. We are interested in the question how the domain size d influences the complexity of deciding satisfiability. We show, assuming the Exponential Time Hypothesis, that two special cases, namely (d,2)-CSP with bounded variable frequency and d-UNIQUE-CSP, already require exponential time Ω(d c·n ) for some c > 0 independent of d. UNIQUE-CSP is the special case for which it is guaranteed that every input constraint system has at most 1 satisfying assignment.Keywords
This publication has 11 references indexed in Scilit:
- Inclusion--Exclusion Algorithms for Counting Set PartitionsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2006
- An LP-Designed Algorithm for Constraint SatisfactionLecture Notes in Computer Science, 2006
- A new algorithm for optimal 2-constraint satisfaction and its implicationsTheoretical Computer Science, 2005
- The complexity of unique k-SAT: an isolation lemma for k-CNFsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2004
- Worst-case time bounds for coloring and satisfiability problemsJournal of Algorithms, 2002
- Which Problems Have Strongly Exponential Complexity?Journal of Computer and System Sciences, 2001
- On the Complexity of k-SATJournal of Computer and System Sciences, 2001
- A condition for matchability in hypergraphsGraphs and Combinatorics, 1995
- Matching is as easy as matrix inversionCombinatorica, 1987
- NP is as easy as detecting unique solutionsTheoretical Computer Science, 1986